Ideais algebricos de aplicações multilineares e polinômios homogêneos

Abstract

The main purpose of this dissertation is the study of ideals of multilinear mappings and homogeneous polynomials between linear spaces. By an ideal we mean a class that is stable under the composition with linear operators. First we study multilinear mappings and spaces of multilinear mappings. We also show how to obtain, from a given multilinear mapping, other multilinear mappings with degrees of multilinearity greater than, equal to or smaller than the degree of the original multilinear mapping. Next we study homogeneous polynomials and spaces of homogeneous polynomials, and we also show how to obtain, from a given n-homogeneous polynomial, other polynomials with degrees of homogeneity greater than, equal to or smaller than the degree of the original polynomial. Next we study ideals of multilinear mappings, or multi-ideals, and ideals of homogeneous polynomial, or polynomial ideals, giving several examples and presenting methods to generated multi-ideals and polynomial ideals from a given operator ideal. Finally we dene and give several examples of coherent multi-ideals and coherent polynomial ideals.